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Solubility of fluvoxamine maleate in supercritical carbon dioxide
Fluid Phase Equilibria 399 (2015) 98–104
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Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d
Solubility of fluvoxamine maleate in supercritical carbon dioxide Yasin Khayyat, [158_TD$IF]Sohrab Moradi Kashkouli, Feridun Esmaeilzadeh [159_TD$IF]* Chemical and Petroleum Engineering Department, School of Engineering, Shiraz University, Iran
A R T I C L E I N F O
A B S T R A C T
Article history: Received 12 October 2014 Received in revised form 28 April 2015 Accepted 29 April 2015 Available online 2 May 2015
During the past decades, processing and engineering the drug particle using new proposed methods have gained an increasing attention. Among the different methods, using supercritical fluids technology is one of the most desired one. In this way, measuring and knowing the solubility of pharmaceuticals in supercritical fluids are one of the most critical parameters must be systematically categorized as a function of pressures and temperatures. Regarding this fact, solubility of fluvoxamine maleate in supercritical carbon dioxide in wide ranges of temperature (308–338 K) and pressure (200–400 bar) was measured using a static method coupled with gravimetric method which is in the range of 1.23 105 to 4.45 104 based on the mole fraction. Finally, the solubility data are modeled using four different semiempirical density-based correlations namely Mendez Santiago-Teja (MST), Bartle et al., Chrastil and Kumar and Johnston (KJ) models. The obtained results reveal that amongst the utilized correlations, Chrastil model leads to the most accurate results compared with the other examined correlations with average absolute relative deviation percent (AARD%) of 10.8%. Besides, the solubility data are modeled using Peng–Robinson equation of state which no satisfactory results are obtained since the AARD% for all of the examined isotherms are in the range of 58.01–67.04%. ã 2015 Published by Elsevier B.V.
Keywords: Fluvoxamine maleate Supercritical carbon dioxide Correlation Static method Gravimetric method
1. Introduction In the past two decades, the researchers are seeking for clean technologies that both reduce pollution or wastes and save energy while the quality of the products get better. One of the most concentered areas for new clean and efficient methods is pharmaceutical engineering and drug delivery industries. Among the different possible and potential processes, supercritical based technologies are the most examined one introduces satisfactory results [1–7]. One of the most important areas of using supercritical-based technologies in pharmaceutical industries is particle engineering which means production of controlled-size particles concomitant with high purity level reduces the risk of remaining solvent residue in the final products. In all of the possible applications of supercritical-based technologies especially particle engineering is knowing the accurate and reliable equilibrium solubility of the pharmaceutical in the supercritical fluids as a function of temperature and pressure even at the absence or presence of co-solvent.
* Corresponding author at: School of Chemical and Petroleum Engineering, Shiraz University, P.O. Box 7134851154, Namazi Square, Shiraz, Iran.Tel.: +98 711 2303071; fax: +98 711 6287294. E-mail address: [email protected] (F. Esmaeilzadeh). http://dx.doi.org/10.1016/j.fluid.2015.04.030 0378-3812/ ã 2015 Published by Elsevier B.V.
In the light of this vital requirement, many researchers have measured the solubility of different compounds in the supercritical fluids especially carbon dioxide (SC–CO2) at the presence or absence of co-solvent extensively. The solubility of compounds in supercritical fluids is highly necessary to establish the technical and economic feasibility of any supercritical fluid-based process [8–16]. Among the different possible solvents, carbon dioxide is extensively used as the solvent due to its unique features including mild critical pressure and temperature, non-toxicity, inflammability, cost effective and its availability make it a good candidate for supercritical-based processes. Among these advantages, mild critical pressure and temperature are the most important since most of the pharmaceutical are not able to tolerate harsh condition of the temperature while carbon dioxide critical temperature is about 31.1 C. On the other hand, although experimental measurement is the most reliable method to obtain the required equilibrium solubility data for designing the processes, it is very costly, time consuming, tedious and even impossible in some cases, to measure the solubility of substances in supercritical carbon dioxide. Respect to this shortcomings, similar to the other fields of sciences, modeling approach and using predictive tools to find the solubility of substances are highly investigated and many several models are proposed including equation of state (EoS) [16–23] and semiempirical correlations [24–29].
Y. Khayyat et al. / Fluid Phase Equilibria 399 (2015) 98–104
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2. Experimental
Among these predictive methods, semi-empirical densitybased correlations are recently gaining increasing attention since using these methods need no knowledge of critical properties and sublimation pressure of substances which are usually unavailable for complex compounds and must be estimated using group contribution methods or other methods introduces unreliability into the prediction results. [160_TD$IF]Semi-empirical correlations utilize several fitting parameters correlate the solubility of compounds [16_TD$IF]only to operational pressure and temperature and density of supercritical fluid.[162_TD$IF] In other words, there is no concern about the uncertainty of the used parameters since it is possible to measure temperature, pressure and density of supercritical fluids with high level of accuracy. According to these advantages, application of these correlations has been increases during the past decades compared to EoS’s. Considering all of these facts and requirements previously discussed, the solubility of fluvoxamine maleate is measured in the current investigation as a function of temperatures (308–338 K) and pressures (200–400 bar). Based on the best knowledge of the authors, there is no reported measured solubility data for fluvoxamine maleate in SC–CO2 in the literature. Fluvoxamine maleate (Luvox) is an antidepressant which functions as a selective serotonin reuptake inhibitor. Fluvoxamine is used for the treatment of major depressive disorder, obsessive compulsive disorder, and anxiety disorders such as panic disorder and post-traumatic stress disorder. In addition, fluvoxamine CR (controlled release) is approved to treat social anxiety disorder. The FDA has added a Black box warning for this drug in reference to increase risks of suicidal thinking and behavior in young adults and children. A study from the Institute for Safe Medication Practices identified reports of violence from those taking fluvoxamine as being 8.4 times higher than expected given the of overall reports for that drug. In addition, several number of side effects have been reported for this drug which makes it application dangerous in some extend. According to these information, it seems that it is applicable to produce controlled-size particles of this medication to reduce its potential risks of usage by reducing the necessary dosage. So, as a preliminary stage, it is necessary to measure the solubility of fluvoxamine maleate in different pressures and temperatures to further see if it is possible to manipulate its particle size or morphology of fluvoxamine maleate using supercritical fluidbased technologies. Finally, the measured solubility data were correlated using four density based correlations namely Bartle et al. [21], Chrastil [26], Kumar and Johnston (KJ) [25], and Mendez Santiago-Teja (MST) [12] and Peng–Robinson EoS as the one of the most important equations utilized for modeling of the solubility data.
2.1. Materials Fluvoxamine maleate (see Table 1) with minimum purity of 98.8% was supplied from Damavand Darou Mgf., Co, Iran and further purified by passing SC–CO2 at 308.15 K and 40 MPa through it for two hours. Additionally, carbon dioxide with minimum purity of 99.8% was supplied from Abughadareh Industrial Gas Company (Shiraz, Iran). Before and after each experiment, the model drug powder was heated up to 318 K in an oven (Behdad, Iran) overnight to ensure no presence of carbon dioxide in samples. 2.2. Experimental procedure In this investigation, a home-made apparatus rated for pressure and temperature up to 60 MPa and 673 K, respectively, is used. This apparatus is equipped with a sapphire window giving the operator the capability of monitoring inside of the equilibrium cell for possible phase transitions. Upon the capability of this apparatus, the solubility of fluvoxamine maleate is measured using a static method coupled with a gravimetric method [29–36] (see Fig. 1). A brief description of solubility measurement of using this apparatus is as follows; at the beginning, CO2 was entered into the upper section of a piston cylinder type displacer. A low friction floating piston inside the cylinder prevents mixing the driving fluid with driven fluid in this case is carbon dioxide. The driving fluid was pressurized by a water-driven oil-free reciprocating manual pump (Haskel Pump, Burbank, USA). The pressure of the displacer was monitored using a pressure gauge (45 MPa) with precision of 0.1 MPa (DEWIT). After increasing the pressure of the CO2 entered into the displacer to a desired pressure it then passed into the homemade piston-cylinder type variable volume cell. The [163_TD$IF]pressure of the equilibrium cell was monitored by a pressure transmitter (0– 40 MPa, WIKA type, Germany) with precision of 0.01 MPa.[164_TD$IF] The point worth-mentioning is that the pressure of the system was maintained constant within 0.5% of the desired value throughout the experiment by continuous monitoring. Besides, a PT-100 resistance thermometer with a precision of 1 K was used to monitor the temperature of the system and a PID controlling method was used to keep the temperature of the equilibrium cell at a desired set point. It must be mentioned that, before any action, for each experiment, 1 g of pure fluvoxamine maleate powder was compacted, (with no additives) in a compactor instrument (Compactor, T555228, Mellat Mashin Sazi Company, Iran) under
Table 1 Physiochemical properties of the fluvoxamine maleate and carbon dioxide. Name
CAS number
Supplier
Purity
Chemical formula
Molar mass (g/mol)
Fluvoxamine maleate
61718-82-9
Damavand Darou Mgf., Co, Iran
98.8%a
C15H21F3N2O2C4H4O4
434.41
Carbon dioxide
124-38-9
Abughadareh Industrial Gas Company, Iran
99.8%b
CO2
a b
based on weight fraction. based on mole fraction.
44.01
Chemical structure
–
100
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a pressure of 2 MPa, to change the powder into a 5 mm diameter tablet. Then, it was wrapped with a tissue and discharged in the equilibrium cell. After charging the sample into the equilibrium cell, the piston inside the cell was moved forward in order to reduce the availability of equilibrium cell as low as possible to evacuate the air inside the equilibrium cell. Then, CO2 was allowed to pass through the equilibrium cell while the outlet valve was opened. After a few seconds, the outlet valve was closed, and the piston inside the equilibrium cell was moved backward to increase the equilibrium cell to its maximum value of 50 cm3. Then, the system was pressurized to a desired value. Note that, as aforementioned, this stage was done in order to evacuate the equilibrium cell from air which might affect the composition of SC–CO2. During the experiments, compacted drug powder was held at constant desired pressure and temperature for about 2.5–3 h while equilibrium cell was shaken gently in order to ensure the attainment of equilibrium. Finally, the equilibrium cell was suddenly depressurized to ambient conditions and remaining drug was weighed to 0.1 mg using a Sartorius BA110S Basic series balance. The potential error due to weighing was 4 wt% since the typical mass of solute for each experiment was greater than 2.5 mg. The volume of supercritical carbon dioxide used in each run was obtained using the volume of the equilibrium cell and the density of the carbon dioxide at the specific pressure and temperature reported previously by Yamini et al. [37]. 2.3. Modeling of solubility data 2.3.1. Semi-empirical correlation method The measured solubility data were correlated using four semiempirical density-based correlations namely MST, KJ, Bartle et al. and Chrastil models. A brief description of the used correlations is given as follow. In the first stage, the Bartle et al. model [21] was used to correlate the solubility of fluvoxamine maleate. The general form of the Bartle et al. [21] model is as below: y p bðKÞ 1 ln 2 ref þ cðkg m3 Þ ðr rref Þ (1) ¼aþ TðKÞ p where a,b and c are fitting parameters, Pref, y and r are the reference pressure of 1 bar, the solute solubility and the density of carbon dioxide at a specific pressure and temperature modified by subtracting 700 kg m3 considering as the reference density, rref, respectively.
The second utilized model was Mendez Santiago and Teja (MST) which is one of the most popular one due to its accuracy and simplicity. In brief, MST has presented an empirical model based on the theory of infinitely dilute solutions [33]. An equation that follows a simple relationship for the solubility of solids in SCFs was deduced: ! y p T ln 2 sub (2) ¼ A þ cr P2 where T is the temperature, y2 is the solubility of the compound in terms of mole fraction, p is the pressure, Psub is the sublimation 2 pressure of solid at temperature T, r is the density of the fluid, and A and c are constants independent of temperature. Since the sublimation pressures are not often available, the proposed model was combined with a Clausius–Clapeyron type expression for the sublimation pressure and a semi-empirical relation, with three adjustable parameters, for the solid solubility was derived: yp 1 T ln (3) ¼ a þ cðkg m3 Þ r þ bðK1 Þ TðKÞ stb p The adjustable parameters of the MST correlation including a, b, and c obtained by performing a simple graphical data fitting to T ln (y2 p/pstd) as a function of (r and T). Finally, solubility data were correlated using Kumar and Johnston method (KJ) and Chrastil model (see Eqs. (4) and (5)). ln y ¼ a þ
bðKÞ 1 1 þ cðm3 kmol Þ rðm3 kmol Þ TðKÞ
(4)
where y is the solubility of the solid, a, b and c are the fitting parameters and r is the density of the supercritical fluid. ln S ¼ a þ
bðKÞ þ c ln r TðKÞ
(5)
where, a, b and c are the fitting parameters and S is the solute solubility in kg m3. Also, the b parameter can be utilized to estimate the solute heat of sublimation (DH sublimation = Rb). Among the above mentioned models, Chrastil method is one of the oldest semi-empirical density-based correlations proposed in 1980s. This correlation was based on this assumption that the solute molecules surrounded by c molecules of a solvent form a solute-solvent complex. In other words, in the Chrastil model
[(Fig._1)TD$IG]
Fig. 1. Schematic diagram of the used apparatus.
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(Eq. (5)), the fitting parameter c indicates the number of solvent molecules surrounding the solute molecule. 2.3.2. Equation of state As aforementioned, besides the semi-empirical correlations, Peng–Robinson EoS was used to model the measured solubility data. Regarding this purpose, the Peng–Robinson EoS coupled with conventional van der Waals mixing rule was used to evaluate the fugacity coefficient of solid in compressed fluid phase. The solubility of a pure solid (component 2) in a supercritical fluid was estimated using the classical expression: y2 ¼
Psub 2
exp scf
PF2
ns2
RT
P
Psub 2
(6)
where, ns2 is the molar volume of the solid component 2, Psub is the 2 sublimation pressure of solute, T and P are the temperature and pressure of the system, respectively and F2 is the fugacity of the
101
Table 3 Measured solubility (y, mole of fluvoxamine maleate/(mole of fluvoxamine maleate + mole of CO2)) of fluvoxamine maleate in supercritical carbon dioxide. P/MPa
y
[157_TD$IF]Standard deviation
Relative standard deviation (%)
T = 308 K 20 24 28 32 36 40
– 1.23 105 1.46 105 1.98 105 2.45 105 2.98 105
– 1.15 106 1.35 106 1.54 106 2.12 106 2.42 106
– 9.35 9.25 7.78 8.65 8.12
T = 318 K 20 24 28 32 36 40
1.87 105 2.74 105 4.01 105 6.01 105 8.02 105 1.10 104
1.73 106 1.92 106 3.61 106 5.09 106 6.32 106 6.30 106
9.25 7.01 9.00 8.47 7.88 5.73
T = 328 K 20 24 28 32 36 40
3.25 105 7.82 105 1.01 104 1.71 104 2.35 104 3.00 104
1.99 106 6.15 106 5.69 106 6.19 106 9.80 106 1.73 105
6.12 7.86 5.63 3.62 4.17 5.75
T = 338 K 20 24 28 32 36 40
3.87 105 1.10 104 2.25 104 3.49 104 4.12 104 4.45 104
3.32 106 8.45 106 9.97 106 1.43 105 1.23 105 2.23 105
8.58 7.68 4.43 4.10 2.99 5.02
scf
solid. In this work, the fugacity coefficient of solute in SC–CO2 F2 was calculated by means of using the Peng–Robinson EoS [38] combined with VDW2 mixing rule. In addition, the lij and kij parameters were optimized using a differential evolution technique using MATLAB software. Differential evolution (DE) is a method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality. In brief, differential evolution is capable of handling non-differentiable, nonlinear and multimodal objective functions. It has been also used to train neural networks having real and constrained integer weights. This kind of solver works iteratively in which at each iteration, called a generation, new vectors are generated by the combination of vectors randomly chosen from the current population (mutation). The resultant vectors are then mixed with a predetermined target vector. This operation is called recombination and produces the trial vector. Finally, the trial vector is accepted for the next generation if and only if it yields a reduction in the value of the objective function. This last operator is referred to as a selection. This procedure continued until the desired error obtained. scf
3. Results and discussion The reliability of the apparatus was previously checked by measuring the solubility (mole fraction, y) of piroxicam in supercritical carbon dioxide at 312.15 K, and the results are listed in Table 2 [29]. The values given in Table 2 were obtained from an arithmetic average of three replicate measurements with relative standard deviations less than 5.8%. This deviation is indicative of the reliability of the method used and the expected accuracy of experimental results obtained. This deviation occurs because the individual equipment errors contribute to the overall error (i.e., pressure, temperature, mass, and volume). In other words, this deviation is due to random experimental errors associated with the difficulties of working with high-pressure supercritical fluids. Regarding to this validation previously performed, the static method coupled with gravimetric technique was used to measure
Maximum solubility uncertainty = 9.84 106. Maximum temperature uncertainty = 0.27 K. Maximum pressure uncertainty = 2.41 bar.
the solubility of fluvoxamine maleate in different temperatures (308–338 K) and pressures (200–400 bar). The obtained results revealed that the solubility of fluvoxamine maleate is in the range of 1.23 105 and 4.45 104 based on the mole fraction. Then, the measured solubility data (see Table 3) were correlated using four semi-empirical density-based correlations including Bartle et al., Chrastil, KJ and MST models. The worth mentioning point is that each individual reported data point is the average of at least three independent measurements. The statistical analysis revealed that the measured solubility data introduces maximum relative standard deviation of 9.35% can raise from the calibration of the instruments or working with high pressures controlling its fluctuations is somehow difficult. In general, the relative standard deviation has its own importance in the field of different sciences and plays a vital role in the calculation and measurement process. Standard deviation is a measure of how precise the average is, that is, how well the individual numbers agree with each other. In total, lower relative standard deviation higher repeatability capability of the measurements means. Relative standard deviation is calculated by dividing the standard deviation of values by the average of the values (see Eq. [165_TD$IF](7)).
Table 2 Comparison of the obtained solubilities of piroxicam with solubilities reported in other literature. Temperature (K)
Pressure (bar)
Macnaughton et al. data [39] solubility (mol solute/mol CO2)
Measured solubility by current method Standard deviation (mol Relative standard (mol solute/mol CO2) [29] solute/mol CO2) deviation (%)
Relative Error (%)
312.15 312.15 312.15 312.15
100 130 160 190
1.3 105 2.08 105 3.12 105 4.41 105
1.21 105 1.92 105 2.92 105 4.23 105
6.92 7.69 6.41 4.08
7.02 107 1.09 106 1.35 106 2.43 106
5.80 5.68 4.62 5.74
102
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Relative standard deviationðRSDÞ 100 standard deviation ¼ avearge of solublity at each point
Table 4 Adjustable parameters of the used semi-empirical density based correlations using graphical data fitting.
(7)
Correlations
As it is obvious in the listed results in Table 3, an increase in the pressure from 200 bar to 400 bar while the temperature held constant leads to an increase in the solubility of fluvoxamine maleate (see Fig. 2). In detail, for four examined isotherms of 308K, 318 K, 328 K and 338 K, increasing pressure from 200 bar to 400 bar increases the solubility by order of 2.42, 5.88, 9.2 and 11.5, respectively. This observed trend can be due to this fact that as the pressure increases the intermolecular distance reduces (density increases) consequently enhances the solvating power which leads to higher solubility of fluvoxamine maleate at the elevated pressures. Besides, mining the obtained results revealed that there is also a strong relation between the solubility and the temperature. But the fact regarding the effect of temperature on the solubility is that the temperature has a dual effect on the solubility by affecting both supercritical fluid density and solute vapor pressure. [16_TD$IF]In more details, as the temperature increases [167_TD$IF]both the density and solute vapor pressure change in different manners. The density of the supercritical fluid decreases [168_TD$IF]as a consequence of temperature enhancement while the solute vapor pressure [169_TD$IF]increases on the other hand. This is the net effect of these two competing factors [170_TD$IF] which dictated the solubility increases or decreases a function of temperature. Based on these facts, it can be concluded that increase of temperature affects solute vapor pressure dominantly compared to the density of SC–CO2 leads to higher solubility of fluvoxamine maleate. At the second stage of this investigation, the measured solubility data were correlated using four semi-empirical density-based correlations namely Bartle et al., Chrastil, KJ and MST models as previously introduced. All of these examined correlations including three fitting parameters must be fitted using least square method or simple graphical data regression which in the current work second approach was used to find the optimum values of the fitting parameters (see Table 3). As it is listed in Table 4, among the four examined correlations, Chrastil model leads to the lowest AARD% of 10.3%, although all of the models lead to a rather similar level of accuracy. In addition, plotting the measured solubility data and those correlated using four different correlations revealed that rather all of these models are able to well correlate the trend of solubility variation as a function of temperature and pressure (see Fig. 3). Finally, the self-consistency tests using four different empirical correlations were performed to find if the measured solubility data
Bartle et al. MST KJ Chrastil
Constants of correlations
AARD%
a
b
c
44.43 21,777 23.41 37.15
16,527 47.64 14,445 14,475
0.01775 5.917 0.5957 12.04
13.7 12.9 12.8 10.8
satisfy the linear behavior of the used correlations or not. In details, if during the self-consistency tests examination, solubility data followed the linear behavior of the used correlations, it can be expected that it is possible to extrapolate the solubility data beyond the investigated temperature and pressure ranges. Regarding this fact, as it can be seen in Fig. 4, measured solubility data are rather able to satisfy the linear behavior of the examined correlations. But a closer examination in the Fig. 4 revealed that as the temperature increases, the used correlation especially KJ model are less able to predict the behavior of the measured solubility data at the elevated temperatures. This observed trend which was previously observed for other
[(Fig._3)TD$IG]
[(Fig._2)TD$IG] -3
10
Solubility (y)
308 K 318 K 328 K 338 K -4
10
-5
10
200
250
300 Pressure/bar
350
400
Fig. 2. Solubility of fluvoxamine maleate in different pressures and temperatures.
Fig. 3. The correlated solubility data of fluvoxamine maleate using different correlations, (a) Chrastil model and (b) KJ model.
Y. Khayyat et al. / Fluid Phase Equilibria 399 (2015) 98–104
[(Fig._4)TD$IG]
103
for predicting the fluvoxamine maleate solubility in different pressures and temperatures. 4. Conclusions
Fig. 4. The self-consistency tests for the four used semi-empirical correlations, (a) MST model, (b) Bartle et al.; and (c) KJ model.
pharmaceuticals [40–43], was reported at first by Kurnik and Reid [44]. In detail, At the high pressures, the density of the of compressed carbon dioxide moves toward a value of 972.3 kg m3 which is not so far away from water at ambient conditions can lead to a phenomenon called “squeezing out”. In other words, at higher pressure and liquid-like densities, the effect of “squeezing out”, that is a retrograde solubility, can often be observed which leads to this fact that the density-based models no longer work willingly in that regions. This phenomenon was firstly reported by Kurnik and Reid [44] while further similar behavior was observed by Kraska et al. [45] for b-carotene solubility. They [17_TD$IF]described this phenomenon based on this fact that the deviation [172_TD$IF]existed between the experimental data [173_TD$IF]and those correlated for pressures above 125 MPa can be due to a special isomerization occurred by an enrichment of cis-isomers in the solution while the all-trans b-carotene is squeezed out of the solution and crystallizes. At last, the solubility of fluvoxamine maleate was correlated using PR-EoS using VDW2 mixing rules as previously described. The two adjustable parameters (kij and lij) were optimized using the DE method using the following objective function [174_TD$IF](see Eq. (8)): AARD% ¼
Exp Calc 100 X jPi Pi j Exp n Pi
(8)
is the experimental solubility and PCalc is the calculated where PExp i i solubility. The required parameters for modeling the solubility of fluvoxamine maleate in SC–CO2 such as critical pressure (18.41 bar) and temperature (1055.921 K) were estimated using Joback method [46]. In addition, the acentric factor (1.55) was estimated using group contribution method proposed by Constantinou and Gani [47]. The obtained adjustable parameters and their errors are given in Table 5. A closer examination of the listed results in Table 5 demonstrated that PR-EoS was not able to correlate the solubility of fluvoxamine maleate in supercritical carbon dioxide willingly compared with the semi-empirical density based correlations. Finally, based on the obtained results during the modeling of fluvoxamine maleate solubility, one can conclude that among the two used different approaches namely semi-empirical correlations and EoS, the first approach is more appropriate to be used reliably
Table 5 The binary interaction parameters for fluvoxamine maleate in SC–CO2 system (VDW2 mixing rule). Temperature (K)
kij
lij
AARD%
308 318 328 338
0.4649 0.4427 0.4104 0.3846
0.09999 0.09999 0.09999 0.09999
58.01 62.89 67.04 65.79
In this current work, solubility of fluvoxamine maleate in supercritical carbon dioxide using a static method coupled with a gravimetric method was measured in different temperatures (308–338 K) and pressures (200–400 bar). The measured solubility data using these method was in the range of 1.23 105 and 4.45 104 based on the mole fraction. The measured solubility data demonstrated a direct relation between the extraction pressure and temperature and solubility of fluvoxamine maleate. The obtained results revealed that in the studied ranges of temperature and pressure no cross over pressure was observed. At last, the measured solubility data were correlated using four semi-empirical density-based correlations namely Bartle et al., MST, KJ and Chrastil models and PR EoS. Calculating the solubility of fluvoxamine maleate by optimized fitting parameters obtained by simple graphical regression showed that it is possible to correlate the solubility of fluvoxamine maleate in the temperature and pressure ranges of 308–338 K and 200–400 bar, respectively, by minimum AARD% of 10.3% using Chrastil model. But on the other hand, the results of modeling using PR EoS method demonstrated that Peng–Robinson EoS is not a good candidate for modeling of fluvoxamine maleate solubility id supercritical carbon dioxide in the temperature and pressure ranges examined in the current investigation. Besides, the results of self-consistency tests using semiempirical density-based correlations demonstrated that all of the four models are able to satisfy the linear behavior of the measured solubility data which can be helpful for extrapolating the solubility of fluvoxamine maleate in different temperatures and pressures. The noteworthy point is that the used empirical correlations encountered with higher deviation as the temperature and pressure increase which was related to the squeezing-out phenomenon. References [1] A.R.C. Duarte, M. Sousa Costa, A.L. Simplício, M.M. Cardoso, C.M.M. Duarte, Int. J. Pharm. 308 (2006) 168–174. [2] P.G. Debenedetti, J.W. Tom, Y. Sang-Do, L. Gio-Bin, J. Control. Release 24 (1993) 27–44. [3] A.R.C. Duarte, T. Casimiro, A. Aguiar-Ricardo, A.L. Simplício, C.M.M. Duarte, J. Supercrit. Fluids 39 (2006) 102–106. [4] Y. Ho Kim, K.S. Shing, Powder Tech. 182 (2008) 25–32. [5] P. Boonnoun, H. Nerome, S. Machmudah, M. Goto, A. Shotipruk, J. Supercrit. Fluids 77 (2013) 103–109. [6] Z. Du, Y.-X. Guan, S.-J. Yao, Z.-Q. Zhu, Int. J. Pharm. 421 (2011) 258–268. [7] L. Zhiyi, J. Jingzhi, L. Xuewu, T. Huihua, W. Wei, J. Supercrit. Fluids 48 (2009) 247–252. [8] T. Kraska, K.O. Leonhard, D. Tuma, G.M. Schneider, J. Supercrit. Fluids 23 (2002) 209–224. [9] A.Z. Hezave, A. Mowla, F. Esmaeilzadeh, J. Supercrit. Fluids 58 (2011) 198–203. [10] T. Nakatani, K. Ohgaki, T. Katayama, J. Supercrit. Fluids 2 (1989) 9–14. [11] Q. Li, Z. Zhang, C. Zhong, Y. Liu, Q. Zhou, Fluid Phase Equilib. 207 (2003) 183– 192. [12] J. Méndez-Santiago, A.S. Teja, Fluid Phase Equilib. 158–200 (1999) 501–510. [13] E. Kosal, C.H. Lee, G.D. Holder, J. Supercrit. Fluids 5 (1992) 169–179. [14] N. Vedaraman, G. Brunner, C.S. Kannan, B.V. Ramabrahmam, P.G. Rao, J. Supercrit. Fluids 30 (2004) 119–125. [15] M. Johannsen, G. Brunner, J. Chem. Eng. Data 40 (2) (1995) 431–434. [16] R. Dohrn, G. Brunner, Fluid Phase Equilib. 106 (1995) 213–282. [17] Z. Huang, Y.C. Chiew, M. Feng, H. Miao, J.-H. Li, Xu. Li, J. Supercrit. Fluids 43 (2007) 259–266. [18] N. Spiliotis, K. Magoulas, D. Tassios, Fluid Phase Equilib. 102 (1994) 121–141. [19] A. Eslamimanesh, F. Esmaeilzadeh, Fluid Phase Equilib. 291 (2010) 141–150. [20] M. Yazdizadeh, A. Eslamimanesh, F. Esmaeilzadeh, J. Supercrit. Fluids 55 (2011) 861–875. [21] K.D. Bartle, A.A. Clifford, S.A. Jafar, J. Phys. Chem. Ref. Data 20 (1991) 713–757. [22] M.D. Gordillo, M.A. Blanco, A. Molero, E. Martinez de la Ossa, J. Supercrit. Fluids 15 (1999) 183–190. [23] J.M. del Valle, J.M. Aguilera, Ind. Eng. Chem. Res. 27 (1988) 1551–1553.
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[24] Y. Adachi, B.C.Y. Lu, H. Sugie, Fluid Phase Equilib. 13 (1983) 133–142. [25] S. Kumar, K.P. Johnston, J. Supercrit. Fluids 27 (1988) 1551–1553. [26] J. Chrastil, Solubility of solids in supercritical gases, J. Phys. Chem. 86 (1982) 3016–3021. [27] D.L. Sparks, R. Hernandez, L.A. Estévez, Chem. Eng. Sci. 63 (2008) 4292–4301. [28] A. Tabernero, E.M.M. del Valle, M.A.A. Galan, J. Supercrit. Fluids 52 (2010) 161– 174. [29] A. Zeinolabedini Hezave, F. Esmaeilzadeh, J. Chem. Eng. Data 57 (2012) 1659– 1664. [30] A. Zeinolabedini Hezave, M. Lashkarbolooki, F. Esmaeilzadeh, J. Supercrit. Fluids 73 (2013) 57–62. [31] A. Zeinolabedini Hezave, S. Aftab, F. Esmaeilzadeh, J. Supercrit. Fluids 68 (2012) 39–44. [32] A. Zeinolabedini Hezave, M.H. Khademi, F. Esmaeilzadeh, Fluid Phase Equilib. 313 (15) (2012) 140–147. [33] A. Zeinolabedini Hezave, A. Mowla, F. Esmaeilzadeh, J. Supercrit. Fluids 58 (2011) 198–203. [34] H. Rajaei, A.Z. Hezave, M. Lashkarbolooki, F. Esmaeilzadeh, J. Supercrit. Fluids 75 (2013) 181–186. [35] M. Ahmadi Sabegh, H. Rajaei, F. Esmaeilzadeh, M. Lashkarbolooki, J. Supercrit. Fluids 72 (2012) 191–197.
[36] S.A. Shojaee, A.Z. Hezave, S. Aftab, M. Lashkarbolooki, F. Esmaeilzadeh, J. Supercrit. Fluids 78 (2013) 1–6. [37] Y. Yamini, M.R. Fat'hi, N. Alizadeh, M. Shamsipur, Fluid Phase Equilib. 152 (1998) 299–305. [38] D.B. Robinson, D.Y. Peng, Ind. Eng. Chem. Fundam. 15 (1976) 59–64. [39] S.J. Macnaughton, I. Kikic, N.R. Foster, P. Alessi, A. Cortesi, I. Colombo, Chem. Eng. Data 41 (1996) 1083–1086. [40] A.Z. Hezave, S. Shahnazar, H. Rajaei, M. Lashkarbolooki, F. Esmaeilzadeh, Fluid Phase Equilib. 355 (2013) 130–134. [41] H. Rajaei, A.Z. Hezave, M. Lashkarbolooki, F. Esmaeilzadeh, J. Supercrit. Fluids 75 (2013) 181–186. [42] M. Lashkarbolooki, A.Z. Hezave, Y. Rahnama, H. Rajaei, Feridun Esmaeilzadeh, J. Supercrit. Fluids [175_TD$IF]684 (2013) 29–35. [43] S.A. Shojaee, H. Rajaei, A.Z. Hezave, M. Lashkarbolooki, F. Esmaeilzadeh, J. Supercrit. Fluids 81 (2013) 42–47. [44] R.T. Kurnik, R.C. Reid, AIChE J. 27 (5) (1981) 861–863. [45] T. Kraska, K.O. Leonhard, D. Tuma, G.M. Schneider, J. Supercrit. Fluids 23 (2002) 209–224. [46] K.G. Joback, R.C. Reid, Chem. Eng. Commun. 57 (1987) 233–243. [47] L. Constantinou, R. Gani, AICHE J. 40 (10) (1994) 1697–1710.
Contents lists available at ScienceDirect
Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d
Solubility of fluvoxamine maleate in supercritical carbon dioxide Yasin Khayyat, [158_TD$IF]Sohrab Moradi Kashkouli, Feridun Esmaeilzadeh [159_TD$IF]* Chemical and Petroleum Engineering Department, School of Engineering, Shiraz University, Iran
A R T I C L E I N F O
A B S T R A C T
Article history: Received 12 October 2014 Received in revised form 28 April 2015 Accepted 29 April 2015 Available online 2 May 2015
During the past decades, processing and engineering the drug particle using new proposed methods have gained an increasing attention. Among the different methods, using supercritical fluids technology is one of the most desired one. In this way, measuring and knowing the solubility of pharmaceuticals in supercritical fluids are one of the most critical parameters must be systematically categorized as a function of pressures and temperatures. Regarding this fact, solubility of fluvoxamine maleate in supercritical carbon dioxide in wide ranges of temperature (308–338 K) and pressure (200–400 bar) was measured using a static method coupled with gravimetric method which is in the range of 1.23 105 to 4.45 104 based on the mole fraction. Finally, the solubility data are modeled using four different semiempirical density-based correlations namely Mendez Santiago-Teja (MST), Bartle et al., Chrastil and Kumar and Johnston (KJ) models. The obtained results reveal that amongst the utilized correlations, Chrastil model leads to the most accurate results compared with the other examined correlations with average absolute relative deviation percent (AARD%) of 10.8%. Besides, the solubility data are modeled using Peng–Robinson equation of state which no satisfactory results are obtained since the AARD% for all of the examined isotherms are in the range of 58.01–67.04%. ã 2015 Published by Elsevier B.V.
Keywords: Fluvoxamine maleate Supercritical carbon dioxide Correlation Static method Gravimetric method
1. Introduction In the past two decades, the researchers are seeking for clean technologies that both reduce pollution or wastes and save energy while the quality of the products get better. One of the most concentered areas for new clean and efficient methods is pharmaceutical engineering and drug delivery industries. Among the different possible and potential processes, supercritical based technologies are the most examined one introduces satisfactory results [1–7]. One of the most important areas of using supercritical-based technologies in pharmaceutical industries is particle engineering which means production of controlled-size particles concomitant with high purity level reduces the risk of remaining solvent residue in the final products. In all of the possible applications of supercritical-based technologies especially particle engineering is knowing the accurate and reliable equilibrium solubility of the pharmaceutical in the supercritical fluids as a function of temperature and pressure even at the absence or presence of co-solvent.
* Corresponding author at: School of Chemical and Petroleum Engineering, Shiraz University, P.O. Box 7134851154, Namazi Square, Shiraz, Iran.Tel.: +98 711 2303071; fax: +98 711 6287294. E-mail address: [email protected] (F. Esmaeilzadeh). http://dx.doi.org/10.1016/j.fluid.2015.04.030 0378-3812/ ã 2015 Published by Elsevier B.V.
In the light of this vital requirement, many researchers have measured the solubility of different compounds in the supercritical fluids especially carbon dioxide (SC–CO2) at the presence or absence of co-solvent extensively. The solubility of compounds in supercritical fluids is highly necessary to establish the technical and economic feasibility of any supercritical fluid-based process [8–16]. Among the different possible solvents, carbon dioxide is extensively used as the solvent due to its unique features including mild critical pressure and temperature, non-toxicity, inflammability, cost effective and its availability make it a good candidate for supercritical-based processes. Among these advantages, mild critical pressure and temperature are the most important since most of the pharmaceutical are not able to tolerate harsh condition of the temperature while carbon dioxide critical temperature is about 31.1 C. On the other hand, although experimental measurement is the most reliable method to obtain the required equilibrium solubility data for designing the processes, it is very costly, time consuming, tedious and even impossible in some cases, to measure the solubility of substances in supercritical carbon dioxide. Respect to this shortcomings, similar to the other fields of sciences, modeling approach and using predictive tools to find the solubility of substances are highly investigated and many several models are proposed including equation of state (EoS) [16–23] and semiempirical correlations [24–29].
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99
2. Experimental
Among these predictive methods, semi-empirical densitybased correlations are recently gaining increasing attention since using these methods need no knowledge of critical properties and sublimation pressure of substances which are usually unavailable for complex compounds and must be estimated using group contribution methods or other methods introduces unreliability into the prediction results. [160_TD$IF]Semi-empirical correlations utilize several fitting parameters correlate the solubility of compounds [16_TD$IF]only to operational pressure and temperature and density of supercritical fluid.[162_TD$IF] In other words, there is no concern about the uncertainty of the used parameters since it is possible to measure temperature, pressure and density of supercritical fluids with high level of accuracy. According to these advantages, application of these correlations has been increases during the past decades compared to EoS’s. Considering all of these facts and requirements previously discussed, the solubility of fluvoxamine maleate is measured in the current investigation as a function of temperatures (308–338 K) and pressures (200–400 bar). Based on the best knowledge of the authors, there is no reported measured solubility data for fluvoxamine maleate in SC–CO2 in the literature. Fluvoxamine maleate (Luvox) is an antidepressant which functions as a selective serotonin reuptake inhibitor. Fluvoxamine is used for the treatment of major depressive disorder, obsessive compulsive disorder, and anxiety disorders such as panic disorder and post-traumatic stress disorder. In addition, fluvoxamine CR (controlled release) is approved to treat social anxiety disorder. The FDA has added a Black box warning for this drug in reference to increase risks of suicidal thinking and behavior in young adults and children. A study from the Institute for Safe Medication Practices identified reports of violence from those taking fluvoxamine as being 8.4 times higher than expected given the of overall reports for that drug. In addition, several number of side effects have been reported for this drug which makes it application dangerous in some extend. According to these information, it seems that it is applicable to produce controlled-size particles of this medication to reduce its potential risks of usage by reducing the necessary dosage. So, as a preliminary stage, it is necessary to measure the solubility of fluvoxamine maleate in different pressures and temperatures to further see if it is possible to manipulate its particle size or morphology of fluvoxamine maleate using supercritical fluidbased technologies. Finally, the measured solubility data were correlated using four density based correlations namely Bartle et al. [21], Chrastil [26], Kumar and Johnston (KJ) [25], and Mendez Santiago-Teja (MST) [12] and Peng–Robinson EoS as the one of the most important equations utilized for modeling of the solubility data.
2.1. Materials Fluvoxamine maleate (see Table 1) with minimum purity of 98.8% was supplied from Damavand Darou Mgf., Co, Iran and further purified by passing SC–CO2 at 308.15 K and 40 MPa through it for two hours. Additionally, carbon dioxide with minimum purity of 99.8% was supplied from Abughadareh Industrial Gas Company (Shiraz, Iran). Before and after each experiment, the model drug powder was heated up to 318 K in an oven (Behdad, Iran) overnight to ensure no presence of carbon dioxide in samples. 2.2. Experimental procedure In this investigation, a home-made apparatus rated for pressure and temperature up to 60 MPa and 673 K, respectively, is used. This apparatus is equipped with a sapphire window giving the operator the capability of monitoring inside of the equilibrium cell for possible phase transitions. Upon the capability of this apparatus, the solubility of fluvoxamine maleate is measured using a static method coupled with a gravimetric method [29–36] (see Fig. 1). A brief description of solubility measurement of using this apparatus is as follows; at the beginning, CO2 was entered into the upper section of a piston cylinder type displacer. A low friction floating piston inside the cylinder prevents mixing the driving fluid with driven fluid in this case is carbon dioxide. The driving fluid was pressurized by a water-driven oil-free reciprocating manual pump (Haskel Pump, Burbank, USA). The pressure of the displacer was monitored using a pressure gauge (45 MPa) with precision of 0.1 MPa (DEWIT). After increasing the pressure of the CO2 entered into the displacer to a desired pressure it then passed into the homemade piston-cylinder type variable volume cell. The [163_TD$IF]pressure of the equilibrium cell was monitored by a pressure transmitter (0– 40 MPa, WIKA type, Germany) with precision of 0.01 MPa.[164_TD$IF] The point worth-mentioning is that the pressure of the system was maintained constant within 0.5% of the desired value throughout the experiment by continuous monitoring. Besides, a PT-100 resistance thermometer with a precision of 1 K was used to monitor the temperature of the system and a PID controlling method was used to keep the temperature of the equilibrium cell at a desired set point. It must be mentioned that, before any action, for each experiment, 1 g of pure fluvoxamine maleate powder was compacted, (with no additives) in a compactor instrument (Compactor, T555228, Mellat Mashin Sazi Company, Iran) under
Table 1 Physiochemical properties of the fluvoxamine maleate and carbon dioxide. Name
CAS number
Supplier
Purity
Chemical formula
Molar mass (g/mol)
Fluvoxamine maleate
61718-82-9
Damavand Darou Mgf., Co, Iran
98.8%a
C15H21F3N2O2C4H4O4
434.41
Carbon dioxide
124-38-9
Abughadareh Industrial Gas Company, Iran
99.8%b
CO2
a b
based on weight fraction. based on mole fraction.
44.01
Chemical structure
–
100
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a pressure of 2 MPa, to change the powder into a 5 mm diameter tablet. Then, it was wrapped with a tissue and discharged in the equilibrium cell. After charging the sample into the equilibrium cell, the piston inside the cell was moved forward in order to reduce the availability of equilibrium cell as low as possible to evacuate the air inside the equilibrium cell. Then, CO2 was allowed to pass through the equilibrium cell while the outlet valve was opened. After a few seconds, the outlet valve was closed, and the piston inside the equilibrium cell was moved backward to increase the equilibrium cell to its maximum value of 50 cm3. Then, the system was pressurized to a desired value. Note that, as aforementioned, this stage was done in order to evacuate the equilibrium cell from air which might affect the composition of SC–CO2. During the experiments, compacted drug powder was held at constant desired pressure and temperature for about 2.5–3 h while equilibrium cell was shaken gently in order to ensure the attainment of equilibrium. Finally, the equilibrium cell was suddenly depressurized to ambient conditions and remaining drug was weighed to 0.1 mg using a Sartorius BA110S Basic series balance. The potential error due to weighing was 4 wt% since the typical mass of solute for each experiment was greater than 2.5 mg. The volume of supercritical carbon dioxide used in each run was obtained using the volume of the equilibrium cell and the density of the carbon dioxide at the specific pressure and temperature reported previously by Yamini et al. [37]. 2.3. Modeling of solubility data 2.3.1. Semi-empirical correlation method The measured solubility data were correlated using four semiempirical density-based correlations namely MST, KJ, Bartle et al. and Chrastil models. A brief description of the used correlations is given as follow. In the first stage, the Bartle et al. model [21] was used to correlate the solubility of fluvoxamine maleate. The general form of the Bartle et al. [21] model is as below: y p bðKÞ 1 ln 2 ref þ cðkg m3 Þ ðr rref Þ (1) ¼aþ TðKÞ p where a,b and c are fitting parameters, Pref, y and r are the reference pressure of 1 bar, the solute solubility and the density of carbon dioxide at a specific pressure and temperature modified by subtracting 700 kg m3 considering as the reference density, rref, respectively.
The second utilized model was Mendez Santiago and Teja (MST) which is one of the most popular one due to its accuracy and simplicity. In brief, MST has presented an empirical model based on the theory of infinitely dilute solutions [33]. An equation that follows a simple relationship for the solubility of solids in SCFs was deduced: ! y p T ln 2 sub (2) ¼ A þ cr P2 where T is the temperature, y2 is the solubility of the compound in terms of mole fraction, p is the pressure, Psub is the sublimation 2 pressure of solid at temperature T, r is the density of the fluid, and A and c are constants independent of temperature. Since the sublimation pressures are not often available, the proposed model was combined with a Clausius–Clapeyron type expression for the sublimation pressure and a semi-empirical relation, with three adjustable parameters, for the solid solubility was derived: yp 1 T ln (3) ¼ a þ cðkg m3 Þ r þ bðK1 Þ TðKÞ stb p The adjustable parameters of the MST correlation including a, b, and c obtained by performing a simple graphical data fitting to T ln (y2 p/pstd) as a function of (r and T). Finally, solubility data were correlated using Kumar and Johnston method (KJ) and Chrastil model (see Eqs. (4) and (5)). ln y ¼ a þ
bðKÞ 1 1 þ cðm3 kmol Þ rðm3 kmol Þ TðKÞ
(4)
where y is the solubility of the solid, a, b and c are the fitting parameters and r is the density of the supercritical fluid. ln S ¼ a þ
bðKÞ þ c ln r TðKÞ
(5)
where, a, b and c are the fitting parameters and S is the solute solubility in kg m3. Also, the b parameter can be utilized to estimate the solute heat of sublimation (DH sublimation = Rb). Among the above mentioned models, Chrastil method is one of the oldest semi-empirical density-based correlations proposed in 1980s. This correlation was based on this assumption that the solute molecules surrounded by c molecules of a solvent form a solute-solvent complex. In other words, in the Chrastil model
[(Fig._1)TD$IG]
Fig. 1. Schematic diagram of the used apparatus.
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(Eq. (5)), the fitting parameter c indicates the number of solvent molecules surrounding the solute molecule. 2.3.2. Equation of state As aforementioned, besides the semi-empirical correlations, Peng–Robinson EoS was used to model the measured solubility data. Regarding this purpose, the Peng–Robinson EoS coupled with conventional van der Waals mixing rule was used to evaluate the fugacity coefficient of solid in compressed fluid phase. The solubility of a pure solid (component 2) in a supercritical fluid was estimated using the classical expression: y2 ¼
Psub 2
exp scf
PF2
ns2
RT
P
Psub 2
(6)
where, ns2 is the molar volume of the solid component 2, Psub is the 2 sublimation pressure of solute, T and P are the temperature and pressure of the system, respectively and F2 is the fugacity of the
101
Table 3 Measured solubility (y, mole of fluvoxamine maleate/(mole of fluvoxamine maleate + mole of CO2)) of fluvoxamine maleate in supercritical carbon dioxide. P/MPa
y
[157_TD$IF]Standard deviation
Relative standard deviation (%)
T = 308 K 20 24 28 32 36 40
– 1.23 105 1.46 105 1.98 105 2.45 105 2.98 105
– 1.15 106 1.35 106 1.54 106 2.12 106 2.42 106
– 9.35 9.25 7.78 8.65 8.12
T = 318 K 20 24 28 32 36 40
1.87 105 2.74 105 4.01 105 6.01 105 8.02 105 1.10 104
1.73 106 1.92 106 3.61 106 5.09 106 6.32 106 6.30 106
9.25 7.01 9.00 8.47 7.88 5.73
T = 328 K 20 24 28 32 36 40
3.25 105 7.82 105 1.01 104 1.71 104 2.35 104 3.00 104
1.99 106 6.15 106 5.69 106 6.19 106 9.80 106 1.73 105
6.12 7.86 5.63 3.62 4.17 5.75
T = 338 K 20 24 28 32 36 40
3.87 105 1.10 104 2.25 104 3.49 104 4.12 104 4.45 104
3.32 106 8.45 106 9.97 106 1.43 105 1.23 105 2.23 105
8.58 7.68 4.43 4.10 2.99 5.02
scf
solid. In this work, the fugacity coefficient of solute in SC–CO2 F2 was calculated by means of using the Peng–Robinson EoS [38] combined with VDW2 mixing rule. In addition, the lij and kij parameters were optimized using a differential evolution technique using MATLAB software. Differential evolution (DE) is a method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality. In brief, differential evolution is capable of handling non-differentiable, nonlinear and multimodal objective functions. It has been also used to train neural networks having real and constrained integer weights. This kind of solver works iteratively in which at each iteration, called a generation, new vectors are generated by the combination of vectors randomly chosen from the current population (mutation). The resultant vectors are then mixed with a predetermined target vector. This operation is called recombination and produces the trial vector. Finally, the trial vector is accepted for the next generation if and only if it yields a reduction in the value of the objective function. This last operator is referred to as a selection. This procedure continued until the desired error obtained. scf
3. Results and discussion The reliability of the apparatus was previously checked by measuring the solubility (mole fraction, y) of piroxicam in supercritical carbon dioxide at 312.15 K, and the results are listed in Table 2 [29]. The values given in Table 2 were obtained from an arithmetic average of three replicate measurements with relative standard deviations less than 5.8%. This deviation is indicative of the reliability of the method used and the expected accuracy of experimental results obtained. This deviation occurs because the individual equipment errors contribute to the overall error (i.e., pressure, temperature, mass, and volume). In other words, this deviation is due to random experimental errors associated with the difficulties of working with high-pressure supercritical fluids. Regarding to this validation previously performed, the static method coupled with gravimetric technique was used to measure
Maximum solubility uncertainty = 9.84 106. Maximum temperature uncertainty = 0.27 K. Maximum pressure uncertainty = 2.41 bar.
the solubility of fluvoxamine maleate in different temperatures (308–338 K) and pressures (200–400 bar). The obtained results revealed that the solubility of fluvoxamine maleate is in the range of 1.23 105 and 4.45 104 based on the mole fraction. Then, the measured solubility data (see Table 3) were correlated using four semi-empirical density-based correlations including Bartle et al., Chrastil, KJ and MST models. The worth mentioning point is that each individual reported data point is the average of at least three independent measurements. The statistical analysis revealed that the measured solubility data introduces maximum relative standard deviation of 9.35% can raise from the calibration of the instruments or working with high pressures controlling its fluctuations is somehow difficult. In general, the relative standard deviation has its own importance in the field of different sciences and plays a vital role in the calculation and measurement process. Standard deviation is a measure of how precise the average is, that is, how well the individual numbers agree with each other. In total, lower relative standard deviation higher repeatability capability of the measurements means. Relative standard deviation is calculated by dividing the standard deviation of values by the average of the values (see Eq. [165_TD$IF](7)).
Table 2 Comparison of the obtained solubilities of piroxicam with solubilities reported in other literature. Temperature (K)
Pressure (bar)
Macnaughton et al. data [39] solubility (mol solute/mol CO2)
Measured solubility by current method Standard deviation (mol Relative standard (mol solute/mol CO2) [29] solute/mol CO2) deviation (%)
Relative Error (%)
312.15 312.15 312.15 312.15
100 130 160 190
1.3 105 2.08 105 3.12 105 4.41 105
1.21 105 1.92 105 2.92 105 4.23 105
6.92 7.69 6.41 4.08
7.02 107 1.09 106 1.35 106 2.43 106
5.80 5.68 4.62 5.74
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Relative standard deviationðRSDÞ 100 standard deviation ¼ avearge of solublity at each point
Table 4 Adjustable parameters of the used semi-empirical density based correlations using graphical data fitting.
(7)
Correlations
As it is obvious in the listed results in Table 3, an increase in the pressure from 200 bar to 400 bar while the temperature held constant leads to an increase in the solubility of fluvoxamine maleate (see Fig. 2). In detail, for four examined isotherms of 308K, 318 K, 328 K and 338 K, increasing pressure from 200 bar to 400 bar increases the solubility by order of 2.42, 5.88, 9.2 and 11.5, respectively. This observed trend can be due to this fact that as the pressure increases the intermolecular distance reduces (density increases) consequently enhances the solvating power which leads to higher solubility of fluvoxamine maleate at the elevated pressures. Besides, mining the obtained results revealed that there is also a strong relation between the solubility and the temperature. But the fact regarding the effect of temperature on the solubility is that the temperature has a dual effect on the solubility by affecting both supercritical fluid density and solute vapor pressure. [16_TD$IF]In more details, as the temperature increases [167_TD$IF]both the density and solute vapor pressure change in different manners. The density of the supercritical fluid decreases [168_TD$IF]as a consequence of temperature enhancement while the solute vapor pressure [169_TD$IF]increases on the other hand. This is the net effect of these two competing factors [170_TD$IF] which dictated the solubility increases or decreases a function of temperature. Based on these facts, it can be concluded that increase of temperature affects solute vapor pressure dominantly compared to the density of SC–CO2 leads to higher solubility of fluvoxamine maleate. At the second stage of this investigation, the measured solubility data were correlated using four semi-empirical density-based correlations namely Bartle et al., Chrastil, KJ and MST models as previously introduced. All of these examined correlations including three fitting parameters must be fitted using least square method or simple graphical data regression which in the current work second approach was used to find the optimum values of the fitting parameters (see Table 3). As it is listed in Table 4, among the four examined correlations, Chrastil model leads to the lowest AARD% of 10.3%, although all of the models lead to a rather similar level of accuracy. In addition, plotting the measured solubility data and those correlated using four different correlations revealed that rather all of these models are able to well correlate the trend of solubility variation as a function of temperature and pressure (see Fig. 3). Finally, the self-consistency tests using four different empirical correlations were performed to find if the measured solubility data
Bartle et al. MST KJ Chrastil
Constants of correlations
AARD%
a
b
c
44.43 21,777 23.41 37.15
16,527 47.64 14,445 14,475
0.01775 5.917 0.5957 12.04
13.7 12.9 12.8 10.8
satisfy the linear behavior of the used correlations or not. In details, if during the self-consistency tests examination, solubility data followed the linear behavior of the used correlations, it can be expected that it is possible to extrapolate the solubility data beyond the investigated temperature and pressure ranges. Regarding this fact, as it can be seen in Fig. 4, measured solubility data are rather able to satisfy the linear behavior of the examined correlations. But a closer examination in the Fig. 4 revealed that as the temperature increases, the used correlation especially KJ model are less able to predict the behavior of the measured solubility data at the elevated temperatures. This observed trend which was previously observed for other
[(Fig._3)TD$IG]
[(Fig._2)TD$IG] -3
10
Solubility (y)
308 K 318 K 328 K 338 K -4
10
-5
10
200
250
300 Pressure/bar
350
400
Fig. 2. Solubility of fluvoxamine maleate in different pressures and temperatures.
Fig. 3. The correlated solubility data of fluvoxamine maleate using different correlations, (a) Chrastil model and (b) KJ model.
Y. Khayyat et al. / Fluid Phase Equilibria 399 (2015) 98–104
[(Fig._4)TD$IG]
103
for predicting the fluvoxamine maleate solubility in different pressures and temperatures. 4. Conclusions
Fig. 4. The self-consistency tests for the four used semi-empirical correlations, (a) MST model, (b) Bartle et al.; and (c) KJ model.
pharmaceuticals [40–43], was reported at first by Kurnik and Reid [44]. In detail, At the high pressures, the density of the of compressed carbon dioxide moves toward a value of 972.3 kg m3 which is not so far away from water at ambient conditions can lead to a phenomenon called “squeezing out”. In other words, at higher pressure and liquid-like densities, the effect of “squeezing out”, that is a retrograde solubility, can often be observed which leads to this fact that the density-based models no longer work willingly in that regions. This phenomenon was firstly reported by Kurnik and Reid [44] while further similar behavior was observed by Kraska et al. [45] for b-carotene solubility. They [17_TD$IF]described this phenomenon based on this fact that the deviation [172_TD$IF]existed between the experimental data [173_TD$IF]and those correlated for pressures above 125 MPa can be due to a special isomerization occurred by an enrichment of cis-isomers in the solution while the all-trans b-carotene is squeezed out of the solution and crystallizes. At last, the solubility of fluvoxamine maleate was correlated using PR-EoS using VDW2 mixing rules as previously described. The two adjustable parameters (kij and lij) were optimized using the DE method using the following objective function [174_TD$IF](see Eq. (8)): AARD% ¼
Exp Calc 100 X jPi Pi j Exp n Pi
(8)
is the experimental solubility and PCalc is the calculated where PExp i i solubility. The required parameters for modeling the solubility of fluvoxamine maleate in SC–CO2 such as critical pressure (18.41 bar) and temperature (1055.921 K) were estimated using Joback method [46]. In addition, the acentric factor (1.55) was estimated using group contribution method proposed by Constantinou and Gani [47]. The obtained adjustable parameters and their errors are given in Table 5. A closer examination of the listed results in Table 5 demonstrated that PR-EoS was not able to correlate the solubility of fluvoxamine maleate in supercritical carbon dioxide willingly compared with the semi-empirical density based correlations. Finally, based on the obtained results during the modeling of fluvoxamine maleate solubility, one can conclude that among the two used different approaches namely semi-empirical correlations and EoS, the first approach is more appropriate to be used reliably
Table 5 The binary interaction parameters for fluvoxamine maleate in SC–CO2 system (VDW2 mixing rule). Temperature (K)
kij
lij
AARD%
308 318 328 338
0.4649 0.4427 0.4104 0.3846
0.09999 0.09999 0.09999 0.09999
58.01 62.89 67.04 65.79
In this current work, solubility of fluvoxamine maleate in supercritical carbon dioxide using a static method coupled with a gravimetric method was measured in different temperatures (308–338 K) and pressures (200–400 bar). The measured solubility data using these method was in the range of 1.23 105 and 4.45 104 based on the mole fraction. The measured solubility data demonstrated a direct relation between the extraction pressure and temperature and solubility of fluvoxamine maleate. The obtained results revealed that in the studied ranges of temperature and pressure no cross over pressure was observed. At last, the measured solubility data were correlated using four semi-empirical density-based correlations namely Bartle et al., MST, KJ and Chrastil models and PR EoS. Calculating the solubility of fluvoxamine maleate by optimized fitting parameters obtained by simple graphical regression showed that it is possible to correlate the solubility of fluvoxamine maleate in the temperature and pressure ranges of 308–338 K and 200–400 bar, respectively, by minimum AARD% of 10.3% using Chrastil model. But on the other hand, the results of modeling using PR EoS method demonstrated that Peng–Robinson EoS is not a good candidate for modeling of fluvoxamine maleate solubility id supercritical carbon dioxide in the temperature and pressure ranges examined in the current investigation. Besides, the results of self-consistency tests using semiempirical density-based correlations demonstrated that all of the four models are able to satisfy the linear behavior of the measured solubility data which can be helpful for extrapolating the solubility of fluvoxamine maleate in different temperatures and pressures. The noteworthy point is that the used empirical correlations encountered with higher deviation as the temperature and pressure increase which was related to the squeezing-out phenomenon. References [1] A.R.C. Duarte, M. Sousa Costa, A.L. Simplício, M.M. Cardoso, C.M.M. Duarte, Int. J. Pharm. 308 (2006) 168–174. [2] P.G. Debenedetti, J.W. Tom, Y. Sang-Do, L. Gio-Bin, J. Control. Release 24 (1993) 27–44. [3] A.R.C. Duarte, T. Casimiro, A. Aguiar-Ricardo, A.L. Simplício, C.M.M. Duarte, J. Supercrit. Fluids 39 (2006) 102–106. [4] Y. Ho Kim, K.S. Shing, Powder Tech. 182 (2008) 25–32. [5] P. Boonnoun, H. Nerome, S. Machmudah, M. Goto, A. Shotipruk, J. Supercrit. Fluids 77 (2013) 103–109. [6] Z. Du, Y.-X. Guan, S.-J. Yao, Z.-Q. Zhu, Int. J. Pharm. 421 (2011) 258–268. [7] L. Zhiyi, J. Jingzhi, L. Xuewu, T. Huihua, W. Wei, J. Supercrit. Fluids 48 (2009) 247–252. [8] T. Kraska, K.O. Leonhard, D. Tuma, G.M. Schneider, J. Supercrit. Fluids 23 (2002) 209–224. [9] A.Z. Hezave, A. Mowla, F. Esmaeilzadeh, J. Supercrit. Fluids 58 (2011) 198–203. [10] T. Nakatani, K. Ohgaki, T. Katayama, J. Supercrit. Fluids 2 (1989) 9–14. [11] Q. Li, Z. Zhang, C. Zhong, Y. Liu, Q. Zhou, Fluid Phase Equilib. 207 (2003) 183– 192. [12] J. Méndez-Santiago, A.S. Teja, Fluid Phase Equilib. 158–200 (1999) 501–510. [13] E. Kosal, C.H. Lee, G.D. Holder, J. Supercrit. Fluids 5 (1992) 169–179. [14] N. Vedaraman, G. Brunner, C.S. Kannan, B.V. Ramabrahmam, P.G. Rao, J. Supercrit. Fluids 30 (2004) 119–125. [15] M. Johannsen, G. Brunner, J. Chem. Eng. Data 40 (2) (1995) 431–434. [16] R. Dohrn, G. Brunner, Fluid Phase Equilib. 106 (1995) 213–282. [17] Z. Huang, Y.C. Chiew, M. Feng, H. Miao, J.-H. Li, Xu. Li, J. Supercrit. Fluids 43 (2007) 259–266. [18] N. Spiliotis, K. Magoulas, D. Tassios, Fluid Phase Equilib. 102 (1994) 121–141. [19] A. Eslamimanesh, F. Esmaeilzadeh, Fluid Phase Equilib. 291 (2010) 141–150. [20] M. Yazdizadeh, A. Eslamimanesh, F. Esmaeilzadeh, J. Supercrit. Fluids 55 (2011) 861–875. [21] K.D. Bartle, A.A. Clifford, S.A. Jafar, J. Phys. Chem. Ref. Data 20 (1991) 713–757. [22] M.D. Gordillo, M.A. Blanco, A. Molero, E. Martinez de la Ossa, J. Supercrit. Fluids 15 (1999) 183–190. [23] J.M. del Valle, J.M. Aguilera, Ind. Eng. Chem. Res. 27 (1988) 1551–1553.
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